Abstract
We consider the delay differential equations \(P'(t) = \frac{{\beta _0 \theta ^n [P(t - \tau )]^j }}{{\theta ^n + [P(t - \tau )]^n }} - \delta P(t),{\rm{ }}j = 0,1,\) which were proposed by Mackey and Glass as a model of blood cell production. We suggest new conditions sufficient for the positive equilibrium of the equation considered to be a global attractor. In contrast to the Lasota-Wazewska model, we establish the existence of the number δj = δj(n, τ) > 0 such that the equilibrium of the equation under consideration is a global attractor for all δ ε (0, δj] independently of β0 and θ.
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Published in Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 1, pp. 5–12, January, 1998.
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Gopalsamy, K., Trofimchuk, S.I. & Bantsur, N.R. A note on global attractivity in models of hematopoiesis. Ukr Math J 50, 3–12 (1998). https://doi.org/10.1007/BF02514684
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DOI: https://doi.org/10.1007/BF02514684